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FA-86396 / Procedural level generation constraints / Open access

Cave smoothing automaton: Automaton reads already-updated rows · case 01

Cave shape depends on scan direction.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Neighbours above the current row are read from the new generation.

VERIFIED REPAIR

Restore `n += grid[rr][cc] == '#'` at the synchronous update step.

Unsuccessful approach: Reading only the up-left block from the new generation still mixes generations.

Case contract

One synchronous step over '#'/'.' rows. For each cell count wall cells among its 8 neighbours (the cell itself excluded); out-of-bounds neighbours count as walls when border_wall. A wall stays a wall when the count is in survive; a floor becomes a wall when the count is in birth. All counts use the input grid.

Why this case matters

Procedural generators silently emit unplayable or unfair levels when a single constraint check uses the wrong boundary, axis, neighborhood or update order; the defect is visible in exact generated geometry.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(grid, birth, survive, border_wall):
    h = len(grid)
    w = len(grid[0])
    out = []
    for r in range(h):
        row = []
        for c in range(w):
            n = 0
            for dr in (-1, 0, 1):
                for dc in (-1, 0, 1):
                    if dr == 0 and dc == 0:
                        continue
                    rr, cc = r + dr, c + dc
                    if 0 <= rr < h and 0 <= cc < w:
                        n += (out[rr][cc] if rr < r else grid[rr][cc]) == '#'
                    elif border_wall:
                        n += 1
            wall = grid[r][c] == '#'
            row.append('#' if (n in survive if wall else n in birth) else '.')
        out.append(''.join(row))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site synchronous update #1', [['###.', '#...'], [3], [2, 3], True], ['....', '....']),
  ('regression synchronous update #1',
   [['....', '###.', '##.#', '....', '.#.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '##.#', '##.#', '#..#', '#.##']),
  ('regression synchronous update #2',
   [['#..#.', '#####', '.#..#', '..##.', '###..', '..#..'], [3], [2, 3], True],
   ['.....', '.....', '.....', '...#.', '.....', '.....']),
  ('regression synchronous update #3',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('control #1', [['.#', '..'], [3], [2, 3], False], ['..', '..'])],
 [('fault site synchronous update #1',
   [['...#', '.#..', '#...', '####'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True],
   ['#..#', '....', '#...', '####']),
  ('regression synchronous update #1',
   [['#..#.', '#####', '.#..#', '..##.', '###..', '..#..'], [3], [2, 3], True],
   ['.....', '.....', '.....', '...#.', '.....', '.....']),
  ('regression synchronous update #2',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('regression synchronous update #3',
   [['.#.#.', '##...', '#.###', '#....', '#..##'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.....', '.##..', '.#...', '...#.', '.....']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('control #1', [['.#', '..'], [3], [2, 3], False], ['..', '..']),
  ('control #2', [['..##.#', '.#####'], [3], [2, 3], True], ['......', '......'])],
 [('regression synchronous update #1',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('regression synchronous update #2',
   [['.#.#.', '##...', '#.###', '#....', '#..##'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.....', '.##..', '.#...', '...#.', '.....']),
  ('regression synchronous update #3',
   [['##.##', '###..', '#.##.', '...##', '#..#.', '##.#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.#...', '####.', '.###.', '...#.', '.....', '.....']),
  ('regression synchronous update #4',
   [['..#.', '..##', '##.#', '.###', '....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '#.##', '####', '#.##', '####']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('control #1', [['..##.#', '.#####'], [3], [2, 3], True], ['......', '......']),
  ('control #2', [['#', '#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True], ['#', '#'])],
 [('fault site synchronous update #1',
   [['##', '#.', '..', '#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True],
   ['##', '##', '..', '##']),
  ('regression synchronous update #1',
   [['##.##', '###..', '#.##.', '...##', '#..#.', '##.#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.#...', '####.', '.###.', '...#.', '.....', '.....']),
  ('regression synchronous update #2',
   [['.#.#.#', '..#..#', '##..#.', '##..#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], False],
   ['......', '..#...', '##....', '##....']),
  ('regression synchronous update #3',
   [['###.', '#..#', '##..', '.#.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '##.#', '#..#', '####']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('control #1', [['.#..##'], [3], [2, 3], True], ['......']),
  ('control #2',
   [['..', '##', '#.', '#.', '##', '.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['##', '##', '##', '##', '##', '##'])],
 [('regression synchronous update #1',
   [['..#.', '..##', '##.#', '.###', '....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '#.##', '####', '#.##', '####']),
  ('regression synchronous update #2',
   [['.#.#.#', '..#..#', '##..#.', '##..#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], False],
   ['......', '..#...', '##....', '##....']),
  ('partial repair boundary #1',
   [['..#..', '.....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#...#', '#...#']),
  ('regression synchronous update #3',
   [['.####.', '.#....', '..#..#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['######', '#.#..#', '###..#']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('control #1', [['.', '.', '#', '.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True], ['#', '#', '#', '#']),
  ('control #2', [['.#', '.#', '##', '#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['..', '..', '..', '..'])]]
for label, args, expected in cases[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
fault site synchronous update #1['....', '..#.']['....', '....']Failed
regression synchronous update #1['####', '####', '####', '#.##', '####']['####', '##.#', '##.#', '#..#', '#.##']Failed
regression synchronous update #2['.....', '.###.', '.#...', '...#.', '.###.', '.....']['.....', '.....', '.....', '...#.', '.....', '.....']Failed
regression synchronous update #3['.##.', '..#.']['.##.', '.##.']Failed
open field corner #1['#.#', '...', '#.#']['#.#', '...', '#.#']Passed
lone pillar #1['...', '...', '...']['...', '...', '...']Passed
dense block #1['.#.', '###', '.#.']['.#.', '###', '.#.']Passed
control #1['..', '..']['..', '..']Passed

SHA-256 / 9c693cc93b4662bad6117487ad177201c796a6a675da0ce67fb0a48546f99810

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(grid, birth, survive, border_wall):
    h = len(grid)
    w = len(grid[0])
    out = []
    for r in range(h):
        row = []
        for c in range(w):
            n = 0
            for dr in (-1, 0, 1):
                for dc in (-1, 0, 1):
                    if dr == 0 and dc == 0:
                        continue
                    rr, cc = r + dr, c + dc
                    if 0 <= rr < h and 0 <= cc < w:
                        n += (out[rr][cc] if rr < r and cc < c else grid[rr][cc]) == '#'
                    elif border_wall:
                        n += 1
            wall = grid[r][c] == '#'
            row.append('#' if (n in survive if wall else n in birth) else '.')
        out.append(''.join(row))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site synchronous update #1', [['###.', '#...'], [3], [2, 3], True], ['....', '....']),
  ('regression synchronous update #1',
   [['....', '###.', '##.#', '....', '.#.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '##.#', '##.#', '#..#', '#.##']),
  ('regression synchronous update #2',
   [['#..#.', '#####', '.#..#', '..##.', '###..', '..#..'], [3], [2, 3], True],
   ['.....', '.....', '.....', '...#.', '.....', '.....']),
  ('regression synchronous update #3',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('control #1', [['.#', '..'], [3], [2, 3], False], ['..', '..'])],
 [('fault site synchronous update #1',
   [['...#', '.#..', '#...', '####'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True],
   ['#..#', '....', '#...', '####']),
  ('regression synchronous update #1',
   [['#..#.', '#####', '.#..#', '..##.', '###..', '..#..'], [3], [2, 3], True],
   ['.....', '.....', '.....', '...#.', '.....', '.....']),
  ('regression synchronous update #2',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('regression synchronous update #3',
   [['.#.#.', '##...', '#.###', '#....', '#..##'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.....', '.##..', '.#...', '...#.', '.....']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('control #1', [['.#', '..'], [3], [2, 3], False], ['..', '..']),
  ('control #2', [['..##.#', '.#####'], [3], [2, 3], True], ['......', '......'])],
 [('regression synchronous update #1',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('regression synchronous update #2',
   [['.#.#.', '##...', '#.###', '#....', '#..##'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.....', '.##..', '.#...', '...#.', '.....']),
  ('regression synchronous update #3',
   [['##.##', '###..', '#.##.', '...##', '#..#.', '##.#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.#...', '####.', '.###.', '...#.', '.....', '.....']),
  ('regression synchronous update #4',
   [['..#.', '..##', '##.#', '.###', '....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '#.##', '####', '#.##', '####']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('control #1', [['..##.#', '.#####'], [3], [2, 3], True], ['......', '......']),
  ('control #2', [['#', '#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True], ['#', '#'])],
 [('fault site synchronous update #1',
   [['##', '#.', '..', '#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True],
   ['##', '##', '..', '##']),
  ('regression synchronous update #1',
   [['##.##', '###..', '#.##.', '...##', '#..#.', '##.#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.#...', '####.', '.###.', '...#.', '.....', '.....']),
  ('regression synchronous update #2',
   [['.#.#.#', '..#..#', '##..#.', '##..#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], False],
   ['......', '..#...', '##....', '##....']),
  ('regression synchronous update #3',
   [['###.', '#..#', '##..', '.#.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '##.#', '#..#', '####']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('control #1', [['.#..##'], [3], [2, 3], True], ['......']),
  ('control #2',
   [['..', '##', '#.', '#.', '##', '.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['##', '##', '##', '##', '##', '##'])],
 [('regression synchronous update #1',
   [['..#.', '..##', '##.#', '.###', '....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '#.##', '####', '#.##', '####']),
  ('regression synchronous update #2',
   [['.#.#.#', '..#..#', '##..#.', '##..#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], False],
   ['......', '..#...', '##....', '##....']),
  ('partial repair boundary #1',
   [['..#..', '.....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#...#', '#...#']),
  ('regression synchronous update #3',
   [['.####.', '.#....', '..#..#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['######', '#.#..#', '###..#']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('control #1', [['.', '.', '#', '.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True], ['#', '#', '#', '#']),
  ('control #2', [['.#', '.#', '##', '#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['..', '..', '..', '..'])]]
for label, args, expected in cases[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
fault site synchronous update #1['....', '....']['....', '....']Passed
regression synchronous update #1['####', '####', '##.#', '#..#', '####']['####', '##.#', '##.#', '#..#', '#.##']Failed
regression synchronous update #2['.....', '.#...', '.#...', '...#.', '...#.', '.....']['.....', '.....', '.....', '...#.', '.....', '.....']Failed
regression synchronous update #3['.##.', '..#.']['.##.', '.##.']Failed
open field corner #1['#.#', '...', '#.#']['#.#', '...', '#.#']Passed
lone pillar #1['...', '...', '...']['...', '...', '...']Passed
dense block #1['.#.', '###', '.#.']['.#.', '###', '.#.']Passed
control #1['..', '..']['..', '..']Passed

SHA-256 / 009f247719b5888e8ac2c5bc09e7f06e5244b30fdb1f5f4fb3e98eaeac5fd52e

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(grid, birth, survive, border_wall):
    h = len(grid)
    w = len(grid[0])
    out = []
    for r in range(h):
        row = []
        for c in range(w):
            n = 0
            for dr in (-1, 0, 1):
                for dc in (-1, 0, 1):
                    if dr == 0 and dc == 0:
                        continue
                    rr, cc = r + dr, c + dc
                    if 0 <= rr < h and 0 <= cc < w:
                        n += grid[rr][cc] == '#'
                    elif border_wall:
                        n += 1
            wall = grid[r][c] == '#'
            row.append('#' if (n in survive if wall else n in birth) else '.')
        out.append(''.join(row))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site synchronous update #1', [['###.', '#...'], [3], [2, 3], True], ['....', '....']),
  ('regression synchronous update #1',
   [['....', '###.', '##.#', '....', '.#.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '##.#', '##.#', '#..#', '#.##']),
  ('regression synchronous update #2',
   [['#..#.', '#####', '.#..#', '..##.', '###..', '..#..'], [3], [2, 3], True],
   ['.....', '.....', '.....', '...#.', '.....', '.....']),
  ('regression synchronous update #3',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('control #1', [['.#', '..'], [3], [2, 3], False], ['..', '..'])],
 [('fault site synchronous update #1',
   [['...#', '.#..', '#...', '####'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True],
   ['#..#', '....', '#...', '####']),
  ('regression synchronous update #1',
   [['#..#.', '#####', '.#..#', '..##.', '###..', '..#..'], [3], [2, 3], True],
   ['.....', '.....', '.....', '...#.', '.....', '.....']),
  ('regression synchronous update #2',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('regression synchronous update #3',
   [['.#.#.', '##...', '#.###', '#....', '#..##'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.....', '.##..', '.#...', '...#.', '.....']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('control #1', [['.#', '..'], [3], [2, 3], False], ['..', '..']),
  ('control #2', [['..##.#', '.#####'], [3], [2, 3], True], ['......', '......'])],
 [('regression synchronous update #1',
   [['###.', '.###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.##.', '.##.']),
  ('regression synchronous update #2',
   [['.#.#.', '##...', '#.###', '#....', '#..##'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.....', '.##..', '.#...', '...#.', '.....']),
  ('regression synchronous update #3',
   [['##.##', '###..', '#.##.', '...##', '#..#.', '##.#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.#...', '####.', '.###.', '...#.', '.....', '.....']),
  ('regression synchronous update #4',
   [['..#.', '..##', '##.#', '.###', '....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '#.##', '####', '#.##', '####']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('control #1', [['..##.#', '.#####'], [3], [2, 3], True], ['......', '......']),
  ('control #2', [['#', '#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True], ['#', '#'])],
 [('fault site synchronous update #1',
   [['##', '#.', '..', '#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True],
   ['##', '##', '..', '##']),
  ('regression synchronous update #1',
   [['##.##', '###..', '#.##.', '...##', '#..#.', '##.#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False],
   ['.#...', '####.', '.###.', '...#.', '.....', '.....']),
  ('regression synchronous update #2',
   [['.#.#.#', '..#..#', '##..#.', '##..#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], False],
   ['......', '..#...', '##....', '##....']),
  ('regression synchronous update #3',
   [['###.', '#..#', '##..', '.#.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '##.#', '#..#', '####']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('lone pillar #1', [['...', '.#.', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['...', '...', '...']),
  ('control #1', [['.#..##'], [3], [2, 3], True], ['......']),
  ('control #2',
   [['..', '##', '#.', '#.', '##', '.#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['##', '##', '##', '##', '##', '##'])],
 [('regression synchronous update #1',
   [['..#.', '..##', '##.#', '.###', '....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['####', '#.##', '####', '#.##', '####']),
  ('regression synchronous update #2',
   [['.#.#.#', '..#..#', '##..#.', '##..#.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], False],
   ['......', '..#...', '##....', '##....']),
  ('partial repair boundary #1',
   [['..#..', '.....'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#...#', '#...#']),
  ('regression synchronous update #3',
   [['.####.', '.#....', '..#..#'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['######', '#.#..#', '###..#']),
  ('dense block #1', [['###', '###', '###'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['.#.', '###', '.#.']),
  ('open field corner #1',
   [['...', '...', '...'], [5, 6, 7, 8], [4, 5, 6, 7, 8], True],
   ['#.#', '...', '#.#']),
  ('control #1', [['.', '.', '#', '.'], [6, 7, 8], [3, 4, 5, 6, 7, 8], True], ['#', '#', '#', '#']),
  ('control #2', [['.#', '.#', '##', '#.'], [5, 6, 7, 8], [4, 5, 6, 7, 8], False], ['..', '..', '..', '..'])]]
for label, args, expected in cases[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
fault site synchronous update #1['....', '....']['....', '....']Passed
regression synchronous update #1['####', '##.#', '##.#', '#..#', '#.##']['####', '##.#', '##.#', '#..#', '#.##']Passed
regression synchronous update #2['.....', '.....', '.....', '...#.', '.....', '.....']['.....', '.....', '.....', '...#.', '.....', '.....']Passed
regression synchronous update #3['.##.', '.##.']['.##.', '.##.']Passed
open field corner #1['#.#', '...', '#.#']['#.#', '...', '#.#']Passed
lone pillar #1['...', '...', '...']['...', '...', '...']Passed
dense block #1['.#.', '###', '.#.']['.#.', '###', '.#.']Passed
control #1['..', '..']['..', '..']Passed

SHA-256 / 45fd4f5ffd66916ef44fdb3c5915e8a490cc0969954a000bca6de2c2c936b8d0

Verification & scope

Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:50:49.281036+00:00.

Case digest / 5ec4cf0d26d3e382df568128a792500b830e72d0dd9ec778564af396b4e64794